The number of zeroes that polynomial $$f(x) = (x-2)^2 + 4$$ can have is:
Correct option is C. 0
$$\textbf{Step 1: Check for what value of x, expression becomes zero.}$$
$$\text{Given,}$$
$$f(x)=(x-2)^2+4$$
$$\text{By observing above equation we can say that it is sum of two positive quantities.}$$
$$\text{As }(x-2)^2 \text{and 4 both are positive terms, it's sum must be positive }$$
$$\text{and we know that sum of two positive term is never zero.}$$
$$\text{Hence, Given expression has no zeroes at all.}$$
$$\textbf{Hence, Option C is correct.}$$